Finite Group DatabasebetaFinite Group Databasebeta| order | 34420 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #20293721⋊C5 |
| Fitting, socle, derived, Sylow | C1721 ⋊ C4×C5 |
| Hall | C1721⋊C5 ⋊ C4 |
| Hall | #20293721 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C1721 | C4×C5 |
| prime radical | D1721⋊C5 | C2 |
| cosocle | D1721 | C2×C5 |
| LCS | G ▷ C1721 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1721 |
Polycyclic presentation:
2,5,2,1721|a^2=c,d^a=d^1248,d^b=d^869,d^c=d^1720106 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34420, 8);